We extend Lévy’s classical criterion for a sequence of
independent identically distributed random variables to belong to the domain of
partial attraction of a nondegenerate Gaussian law to stationary $\phi$-mixing
sequences. We also extend some results of Kesten and of Kuelbs and Zinn on the
LIL behavior of independent identically distributed random variables to
stationary $\phi$-mixing sequences. No assumptions on the rate of decay for the
mixing coefficient are made.
Publié le : 1998-04-14
Classification:
Domain of attraction,
mixing,
central limit theorem,
law of the iterated logarithm,
60F05,
60F12,
60F17
@article{1022855651,
author = {Berkes, Istv\'an and Philipp, Walter},
title = {Limit theorems for mixing sequences without rate
assumptions},
journal = {Ann. Probab.},
volume = {26},
number = {1},
year = {1998},
pages = { 805-831},
language = {en},
url = {http://dml.mathdoc.fr/item/1022855651}
}
Berkes, István; Philipp, Walter. Limit theorems for mixing sequences without rate
assumptions. Ann. Probab., Tome 26 (1998) no. 1, pp. 805-831. http://gdmltest.u-ga.fr/item/1022855651/